43.7.4 problem 4(d)

Internal problem ID [8929]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 74
Problem number : 4(d)
Date solved : Tuesday, September 30, 2025 at 06:00:16 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-i y^{\prime \prime }+4 y^{\prime }-4 i y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

ode:=diff(diff(diff(y(x),x),x),x)-I*diff(diff(y(x),x),x)+4*diff(y(x),x)-4*I*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{2 i x}+c_2 \,{\mathrm e}^{-2 i x}+c_3 \,{\mathrm e}^{i x} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 36

ode=D[y[x],{x,3}]-I*D[y[x],{x,2}]+4*D[y[x],x]-4*I*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-2 i x} \left (c_2 e^{4 i x}+c_3 e^{3 i x}+c_1\right ) \end{align*}

✓ Sympy. Time used: 1.036 (sec). Leaf size: 857

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(complex(0, -4)*y(x) + complex(0, -1)*Derivative(y(x), (x, 2)) + 4*Derivative(y(x), x) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \text {Solution too large to show} \]